Remark 8.11 After earlier versions of this article and the sequel [1]} were posted on arXiv, the semiclassical Weyl's law (REF ) was established for \(n\ge 3\)  and \(p=n/2\)  by the first named author in a joint preprint with F. Sukochev and D. Zanin (see [2]}). The cases \(n=2\)  or \(p\ne n/2\) , as well as the curved version conjectured in [1]}, still remain open to date.

